Which expression is equivalent to (5^9)^3? Choices: (A)1/5^27 (B)5^27 (C)1/5^12 (D)5^12

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. When we raise a power to another power, we multiply the exponents. (a^m)^n = a^(m*n)Apply Rule to Calculation: Apply the exponent rule to (5^9)^3. We multiply the exponents 9 and 3. (5^9)^3 = 5^(9*3) = 5^27Choose Equivalent Expression: Choose the equivalent expression for (5^9)^3. From the calculation in Step 2, we know that (5^9)^3 is equivalent to 5^27.

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Which expression is equivalent to $(5^9)^3$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{5^{27}}$ $\newline$ (B) $5^{27}$ $\newline$ (C) $\frac{1}{5^{12}}$ $\newline$ (D) $5^{12}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions I

Full solution

Q. Which expression is equivalent to

(5^9)^3

\newline

Choices:

\newline

(A)

\frac{1}{5^{27}}

\newline

(B)

5^{27}

\newline

(C)

\frac{1}{5^{12}}

\newline

(D)

5^{12}

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When we raise a power to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m*n)}$
Apply Rule to Calculation: Apply the exponent rule to $(5^9)^3$ . We multiply the exponents $9$ and $3$ . $(5^9)^3 = 5^{(9*3)} = 5^{27}$
Choose Equivalent Expression: Choose the equivalent expression for $(5^9)^3$ . From the calculation in Step $2$ , we know that $(5^9)^3$ is equivalent to $5^{27}$ .